Question

extrema and average rates of change assignment

1. ( f(x) = -x^2 - 3x + 4 ) (-3; 2)

solve the problem

1. maria records her distance from home over time. the values are shown in the table below. find her average speed over the first 4 hours.

( t ) (hours)	0	1	2	3	4	5	6	7

Explanation:

Step1: Recall the formula for average speed

The average speed is given by the total distance traveled divided by the total time taken. The formula is $\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$.

Step2: Identify the total distance and total time for the first 4 hours

From the table, at $t = 0$ hours, $D(0)=0$ miles (starting point), and at $t = 4$ hours, $D(4) = 220$ miles. The total time is $4 - 0=4$ hours, and the total distance traveled is $D(4)-D(0)=220 - 0 = 220$ miles.

Step3: Calculate the average speed

Using the formula for average speed, we substitute the total distance and total time: $\text{Average Speed}=\frac{220}{4}$.

Step4: Simplify the expression

$\frac{220}{4}=55$.

Answer:

55 miles per hour